Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22589176 | C2 | semidirect |
| 3. #22588365 | C2 | semidirect |
| 4. #22586909 | C2 | semidirect |
| 5. C71×#1752 | C2 | semidirect |
| 6. C22×D568 | C4 | semidirect |
| 12. C2×#14556062 | C4 | semidirect |
| 14. C2×#14556050 | C4 | semidirect |
| 146. C8×C71 | #99 | semidirect |
| 181. #1752 | D71 | semidirect |
| 183. C71 | #9785 | semidirect |
| 324. C8 | #14556042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986235 | 2 |
| #22589176 | 2 |
| #22588365 | 2 |
| #22586909 | 2 |
| C71×#1752 | 2 |
| #9785 | 71 |